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The present paper deals with the characterization of a new submersion named semi-invariant conformal $\zeta ^{\perp }$-Riemannian submersion from almost contact metric manifolds onto Riemannian manifolds which is the generalization of some known submersions on Riemannian manifolds. We give important and adequate conditions for such submersions to be totally geodesic and harmonic. Also, few examples are examined for such submersions endowed with horizontal Reeb vector field.

In this paper, we present a classification of $ N(\kappa)$-contact metric manifolds with using some special flatness conditions on $ \mathcal{T} $-curvature tensor. We examine $\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, $ \xi$-$\mathcal{T}$-flat and $ \varphi $-$\mathcal{T}$-flat $ N(\kappa)$-contact metric manifolds .Also,we consider the conditions $ \mathcal{T}(\xi,X).R=0 $ and $ \mathcal{T}(\xi,X).S=0 $ for the Riemannian curvature tensor $ R $ and Ricci curvature tensor $ S $. Thus, we obtain a classification of $ N(\kappa)$-contact metric manifolds., Comment: arXiv admin note: text overlap with arXiv:2004.02536

In this paper, we present a classification of $ N(��)$-contact metric manifolds with using some special flatness conditions on $ \mathcal{T} $-curvature tensor. We examine $\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, $ ��$-$\mathcal{T}$-flat and $ ��$-$\mathcal{T}$-flat $ N(��)$-contact metric manifolds .Also,we consider the conditions $ \mathcal{T}(��,X).R=0 $ and $ \mathcal{T}(��,X).S=0 $ for the Riemannian curvature tensor $ R $ and Ricci curvature tensor $ S $. Thus, we obtain a classification of $ N(��)$-contact metric manifolds., arXiv admin note: text overlap with arXiv:2004.02536

The object of the present paper is to study the geometric properties of Concircular curvature tensor on Lorentzian $\alpha -$Sasakian manifold admitting a type of quarter-symmetric metric connection. In the last, we provide an example of 3-dimensional Lorentzian $\alpha -$Sasakian manifold endowed with the quarter-symmetric metric connection which is under consideration is an $\eta -$Einstein manifold with respect to the quarter-symmetric metric connection.